Jeremy L

Timing: Approximately 5 weeks Across this series, you are asked to solve systems of equations in support of two goals: to determine the solution to the system of equations and to become strategic and efficient in choosing a method to solve the system. You use systems of linear equations and systems of linear inequalities to model physical phenomena, especially those with multiple constraints where an optimal solution to an objective function is desired. Through these contexts, you build upon your prior knowledge of solving systems of equations and develop more sophisticated understandings about what the solution(s) to a system means in the context of the problem. ENDURING UNDERSTANDINGS You will understand that ... - A solution to a system of linear equations or inequalities is an ordered pair of numbers that satisfies all the equations or inequalities simultaneously. - Solving a system of linear inequalities or inequalities is a process of determining the value or values that make the equation or inequality true. - Systems of linear equations or inequalities can be used to model scenarios that include multiple constraints, such as resource limitations, goals, comparisons, and tolerances. KEY CONCEPTS - 1: The solution to a system of equation - 2: Solving a system of linear equations algebraically - 3: Modelling with systems of linear equations - 4: Systems of linear inequalities

Timing: Approximately 9 weeks Linear relationships are among the most prevalent and useful relationships to mathematics and the real world. Any inequality in two variables that exhibits a constant rate of change for these variables is linear. Real-world contexts that have a constant rate of change and data sets with a nearly constant rate of change can be effectively modelled by a linear function. You will explore all aspects of linear relationships in this series: contextual problems that involve constant rate of change, lines in the coordinate plane, arithmetic sequences, and algebraic means of expressing a linear relationship between two quantities. Through this series, you will develop deep skills with linear functions and equations and an appreciation for the simplicity and power of linear functions as building blocks of all higher mathematics. ENDURING UNDERSTANDINGS You will understand that ... - A linear relationship has a constant rate of change, which can be visualised as the slope of the associated graph. - There are many ways to algebraically represent a linear function and each form reveals different aspects of the function. - Linear functions can be used to model contextual scenarios that involve a constant rate of change or data whose general trend is linear. - A solution to a two-variable linear equation or inequality is an ordered pair that makes the equation or inequality true. KEY CONCEPTS - 1: Constant rate of change and slope - 2: Linear functions - 3: Linear equations - 4: Linear models of nonlinear scenarios - 5: Two-variable linear inequalities